Abstract

The site-bond percolation problem in two-dimensional (3,122) lattices has been studied by means of numerical simulation and analytical calculations. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B and S∪B) were considered. In S∩B (S∪B), two points are connected if a sequence of occupied sites AND (OR) bonds joins them. The analytical method is based on the approximation introduced by Tsallis (2004), which allows to calculate the S∩B and S∪B percolation functions from the percolation functions corresponding to pure site and pure bond percolation problems. Theoretical and numerical data (supplemented by analysis using finite-size scaling theory) were used to determine, for the first time, the complete phase diagram of the system (phase boundary between the percolating and nonpercolating regions). Comparisons between results obtained using the Tsallis's scheme and simulation data were performed in order to test the reaches and limitations of the approach developed here.